# Talk:Detect division by zero

## division of zero by zero

Many of the solutions here simply check that the result is infinite. This will fail if the numerator is 0 too, since 0 / 0 is mathematically incalculable (many languages return NaN here).

A correct pseudocode solution is:

result = numerator / denominator
if numerator equals 0
if result is not a number
divide by zero action
end
else
if result is infinite
divide by zero action
end
end

0 / 0 is NOT mathematically incalculable -- it is trivially calculable. The problem with 0 / 0 is that any numerical answer is a valid answer. In other words NaN is not a valid result for 0 / 0 but is a description of the character of those answers. (The result can be any of an infinite variety of numbers and not just "a" single number.) This is a problem in mathematics because the result, by itself, is not sufficient to prove anything. Thus, we at times use limits and other constructs to reason about cases involving 0 / 0. A less deceptive result than NaN for 0 / 0 would be "Any Number", but to my knowledge no languages implement that. --Rdm 18:19, 18 June 2010 (UTC)
Maybe it's correct as multiple numbers are Not a Number :-)
(Being pedantic seems to be catching). --Paddy3118 18:37, 18 June 2010 (UTC)
"In other words NaN is not a valid result for 0 / 0 but is a description of the character of those answers." --Rdm 19:17, 18 June 2010 (UTC)
I don't know what "mathematically incalculable" means, but I can testify that in pure mathematics, division by zero, regardless of the dividend, is undefined. Expressions such as $\lim_{x \to 0} \frac{x^2}{x}$ , though they may appear to involve division by zero, actually don't. This expression, for instance, means "the number y such that for all positive ε there exists a positive δ such that for all $x \in (-\delta, \delta)$ , $\left|\frac{x^2}{x} - y\right| < \epsilon$ ", i.e., 0. —Underscore (Talk) 01:04, 19 June 2010 (UTC)
According to the wikipedia "In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible, and unambiguous values. Whether an expression has a meaningful value depends on the context of the expression. For example the value of 4 − 5 is undefined if a positive integer result is required." And the problem with 0/0 is the cardinality of the result, not the lack of any results. --Rdm 11:37, 19 June 2010 (UTC)
I don't know of any conventional mathematical context in which "$\frac{1}{0}$ " or "$\frac{0}{0}$ " has a meaningful, sensible, and unambiguous value. —Underscore (Talk) 18:42, 19 June 2010 (UTC)
I thought 1/0 was often accepted to represent an infinity, though I can agree that infinities are not necessarily sensible nor unambiguous. That said, mathematics seems capable of dealing with such subjects. --Rdm 02:58, 20 June 2010 (UTC)
Limits are such a context. $\lim_{n\rightarrow+0}\frac 10$ converges to (positive) infinity. It's not actually a value per se. When performing operations and calculations this if often not done precisely (by handling the limits) but for the most part that doesn't really matter. Still, ∞ isn't part of the real numbers. —Johannes Rössel 09:27, 20 June 2010 (UTC)
Ok, but everything in mathematics is based on context, though of course the interesting math is relevant in a wide variety of contexts. Nevertheless, we also have areas of mathematics where an operation logically could give any of an infinite set of results and for convenience we pick one of those results as the for that expression. One might argue that having the value of 0 for the principle value for 0/0 is not useful, but in my opinion this is akin to saying that 0 itself is not useful. Note, for example, that this approach would usually eliminate the need for knuth's "strong zero" approach at http://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf Of course, exceptions can be constructed but they can be dealt with in much the same way as any other case that requires the use of a non-principal value. --Rdm 15:02, 2 July 2010 (UTC)

## Choices in Javascript Implementation

Can someone provide reasoning for the way JavaScript solution is implemented? To me it looks like it is simply passing back the JS result and returning 0 if the expression evaluates to NaN. It also return 0 for divByZero(4,'n'). I think we can all agree diving by a string is not 0 :). I wrote a solution but don't want to add it in case I'm not completely understanding the function :) My solution
   function divzero(l,r) {
return ((l/r).toString() === 'Infinity' || (l/r).toString()  === '-Infinity' || (l/r).toString() === 'NaN') ? "error" : l/r
}


Tested Chrome & Firefox, The methods used are in ECMA since JS 2.0. Tested with 4/2 return 2, 4/0 returns error, 4/-0 return error, 0,0 returns error, 0,n returns error, 0,4 returns 0 --Nycigor (talk) 00:02, 6 November 2015 (UTC)

The task asks that division by zero be detected, but leaves open what to do at that point. The decision to return zero should be seen not as detection but as an (arbitrary but silly) decision about what to do after detection. --Rdm (talk) 14:40, 6 November 2015 (UTC)

## divides by zero

Math:

It's all fun and games until somebody divides by zero.       -- Gerard Schildberger (talk) 13:47, 30 November 2019 (UTC)